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Morse theory

In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find CW…

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Formal development

Morse–Bott theory

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Morse theory

Nodes82
Edges81
Triples93
Avg. degree1.98
Density0.02439
Components1

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Morse theory

Top relations

related to Further reading · 62
Morse theory → American Mathematical Society, American Mathematical Society Colloquium, An Introduction, Antoni, Arthur, Birkhäuser, Bott, Bulletin, Cayley, CS1, Dales, Date, Differential Geometry, Differential Manifolds, Differential Topology, Dover Book, Dover Publications, Fundamentals, Graduate Texts, Guest
see also · 12
Morse theory → Almgren, Aspect, Combinatorial, Digital, Grassmannian, Mathematical, Morse, Pitts, Schnirelmann, Smale, Theorem, Type
related to Morse inequalities · 10
Morse theory → Also, Betti, CW, Euler, In, Morse, The, Therefore, These, Using
related to Fundamental theorems · 5
Morse theory → As, Half, Morse, Technically, This
related to Application to classification of closed 2-manifolds · 4
Morse theory → If, In, Morse, RP

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Important terminology

displaystyle morse critical theory point manifold points function index homology topology one bott non-degenerate manifolds passes gamma functions theorem differential

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Morse theoryrelated to Application to classification of closed 2-manifoldsMorse0.60section
Morse theoryrelated to Application to classification of closed 2-manifoldsIf0.60section
Morse theoryrelated to Application to classification of closed 2-manifoldsRP0.60section
Morse theoryrelated to Application to classification of closed 2-manifoldsIn0.60section
Morse theoryrelated to Fundamental theoremsMorse0.60section
Morse theoryrelated to Fundamental theoremsTechnically0.60section
Morse theoryrelated to Fundamental theoremsThis0.60section
Morse theoryrelated to Fundamental theoremsAs0.60section
Morse theoryrelated to Fundamental theoremsHalf0.60section
Morse theoryrelated to Further readingBott0.60section
Morse theoryrelated to Further readingRaoul0.60section
Morse theoryrelated to Further readingMorse Theory Indomitable0.60section

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